Question

Consider that the 1${}^{st}$ triangular number is 1, 2${}^{nd}$ triangular number is 3, 3${}^{rd}$ triangular number is 6 and so on. The 26${}^{th}$ triangular number is 351. Determine the 25${}^{th}$ triangular number.

Answer 1

A $n^{th}$ triangular number is essentially the sum of the first $n$ natural numbers.

$1=1$
$3=1+2$
$6=1+2+3$
.
.
.
and, so on

The 26${}^{th}$ triangular number can be written as
$1+2+3+..........+24+25+26=351$

The sum of the first 25 numbers is the 25${}^{th}$ triangular number, so
25${}^{th}$ triangular number $+26=351$

Hence, 25${}^{th}$ triangular number $=325$